Question

Write the system of equations shown on each graph, then give the solution to the system.

Answer 1

Explanation:

Question 1.

Slope of line 'l' =
`\frac{\text{Rise}}{\text{Run}}`

=
`(8)/(6)`

=
`(4)/(3)`

Equation of a line passing through (x', y') and slope 'm' is,

y - y' = m(x - x')

Since, line 'l' is passing through (0, 7) and slope =
`(4)/(3)`

Equation will be,

y - 7 =
`(4)/(3)(x-0)`

y =
`(4)/(3)x+7`

Similarly, slope of line m =
`\frac{\text{Rise}}{\text{Run}}`

=
`(-3)/(6)`

=
`-(1)/(2)`

Therefore, equation of line 'm' passing through point (0, -4) will be,

y + 4 =
`-(1)/(2)(x - 0)`

y =
`-(1)/(2)x-4`

Solution = Point of intersection of both the lines

= (-6, -1)

Question 2

Slope of line 'l' =
`\frac{\text{Rise}}{\text{Run}}`

=
`(-2)/(5)`

Equation of line 'l' passing through a point (0, 4) and slope = -
`(2)/(5)`

y - 4 =
`-(2)/(5)(x-0)`

y =
`-(2)/(5)x+4`

Slope of line 'm' =
`\frac{\text{Rise}}{\text{Run}}`

=
`(-2)/(5)`

Equation of line 'm' passing through a point (0, -1) and slope =
`-(2)/(5)`

y + 1 =
`-(2)/(5)(x-0)`

y =
`-(2)/(5)x-1`

Since, slopes of both the lines are same, these lines will be parallel.

There will be NO SOLUTION.